5 Best Ways to Return the Cumulative Product of Array Elements Treating NaNs as One in Python

💡 Problem Formulation: When dealing with numerical data in Python, it’s common to encounter arrays with NaN (Not a Number) values. In processing such arrays, one might need to compute the cumulative product of the elements while treating NaNs as if they were ones, thus ignoring them in the computation. For example, given the input array [3, NaN, 4, NaN, 2], the desired output would be [3, 3, 12, 12, 24]. This article will explore different methods to achieve this in Python.

Method 1: Using NumPy with nan_to_num

This method relies on the NumPy library, which is well-suited for numerical computations in Python. The function numpy.cumprod() computes the cumulative product of array elements. Combined with numpy.nan_to_num(), which substitutes NaNs with specified values, we achieve the required functionality.

Here’s an example:

import numpy as np

def cumulative_product_ignore_nans(array):
    clean_array = np.nan_to_num(array, nan=1.0)
    return np.cumprod(clean_array)
    
example_array = np.array([3, np.nan, 4, np.nan, 2])
print(cumulative_product_ignore_nans(example_array))

Output:

[ 3.  3. 12. 12. 24.]

The function cumulative_product_ignore_nans first replaces any NaNs in the input array with ones using np.nan_to_num. The cumulative product of the cleaned array is then computed with np.cumprod, resulting in the expected output.

Method 2: Using NumPy Masking

Method 2 also uses NumPy but with a different approach – masking. With NumPy, NaN values can be effectively masked, essentially ignoring them in subsequent operations without altering the original data.

Here’s an example:

import numpy as np

def cumulative_product_with_masking(array):
    masked_array = np.where(np.isnan(array), 1, array)
    return np.cumprod(masked_array)
    
example_array = np.array([3, np.nan, 4, np.nan, 2])
print(cumulative_product_with_masking(example_array))

Output:

[ 3.  3. 12. 12. 24.]

The function cumulative_product_with_masking uses np.where to create a version of the array where NaNs are replaced by ones. The cumulative product is then taken over this masked array to return the desired result.

Method 3: Using pandas cumprod

Pandas provides high-level data manipulation tools for Python. Within pandas, NaN values are treated as ‘non-existent’ in certain operations such as pd.Series.cumprod() which calculates the cumulative product, naturally skipping over NaNs.

Here’s an example:

import pandas as pd

def cumulative_product_with_pandas(array):
    series = pd.Series(array).fillna(1)
    return series.cumprod().to_numpy()
    
example_array = np.array([3, np.nan, 4, np.nan, 2])
print(cumulative_product_with_pandas(example_array))

Output:

[ 3.  3. 12. 12. 24.]

The function cumulative_product_with_pandas converts the array to a pandas Series, replaces NaNs with ones using fillna(1), computes the cumulative product, and finally converts the result back to a NumPy array.

Method 4: Custom Cumulative Product Function

For environments where NumPy or pandas may not be available, a custom function can be written to iterate through the array, treating NaNs as ones and computing the cumulative product manually.

Here’s an example:

import math

def cumulative_product_custom(array):
    cum_product = 1
    result = []
    for num in array:
        if not math.isnan(num):
            cum_product *= num
        result.append(cum_product)
    return result
    
example_array = [3, float('nan'), 4, float('nan'), 2]
print(cumulative_product_custom(example_array))

Output:

[3, 3, 12, 12, 24]

The function cumulative_product_custom iterates over the array multiplying non-NaN numbers to a running product and appending the current product to the result list. NaNs are effectively treated as ones since they do not alter the running product.

Bonus One-Liner Method 5: Using NumPy with NaN Product Trick

A sleek one-liner that leverages NumPy’s natural handling of NaNs in multiplication by directly using the np.cumprod() function on the array after having NaN values replaced with ones.

Here’s an example:

import numpy as np

example_array = np.array([3, np.nan, 4, np.nan, 2])
cum_product = np.cumprod(np.where(np.isnan(example_array), 1, example_array))
print(cum_product)

Output:

[ 3.  3. 12. 12. 24.]

The one-liner performs a conditional replacement of NaNs with ones using np.where, directly followed by np.cumprod() to get the cumulative product in a concise manner.

Summary/Discussion

• Method 1: NumPy with nan_to_num. Strengths: Simple, efficient, and utilizes widely used numerical library. Weaknesses: Requires NumPy, which might not be available in all environments.
• Method 2: NumPy Masking. Strengths: Avoids altering the original array and is quite intuitive. Weaknesses: Similar to Method 1, relies on the availability of NumPy.
• Method 3: pandas cumprod. Strengths: Utilizes pandas’ built-in functionality, elegant and concise. Weaknesses: Requires pandas, more overhead for simple tasks compared to NumPy methods.
• Method 4: Custom Cumulative Product Function. Strengths: No external dependencies, highly customizable. Weaknesses: Potentially less performant compared to library-based solutions.
• Bonus One-Liner Method 5: Strengths: Very concise. Weaknesses: Might be less readable for beginners; depends on NumPy.